Performance Optimization via Sequential Processing for Nonlinear State Estimation of Noisy Systems

Abstract

We propose a framework for designing observers for noisy nonlinear systems with global convergence properties and performing robustness and noise sensitivity. This framework comes out from the combination of a state norm estimator with a chain of filters, adaptively tuned by the state norm estimator. The state estimate is sequentially processed through the chain of filters. Each filter contributes to improve by a certain amount the estimation error performances of the previous filter in terms of noise sensitivity and this amount is quantitatively evaluated using a comparison criterion which considers the ratio of the asymptotic error norm bounds of two consecutive filters in the chain. A recursive algorithm is given for implementing the chain of filters and guaranteeing a sequential error performance optimization process. Simulations show the effectiveness of these chains of filters.

Towards improving the estimation performance of a given nonlinear observer: a multi-observer approach

“…In this context, an alternative consists in aiming at improving the estimation performance of a given observer. To the best of the authors' knowledge, existing works in this direction either concentrate on specific classes of systems (see e.g., [4]- [6] for linear systems or e.g., [7]- [12] in the context of high-gain observers) or on specific properties like robustness to measurement noise (see, e.g., [13], [14]) or the reduction of the undesired effect of the peaking phenomenon (see e.g., [15] for a general approach and [8], [10], [12] for specific solutions in the context of high-gain observer). An exception is [16], where two observers designed for a general nonlinear system are "united" to exploit the good properties of each.…”